Paper by Erik D. Demaine

Glencora Borradaile, Erik D. Demaine, and Siamak Tazari, “Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs”, in Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009), Freiburg, Germany, February 26–28, 2009, pages 171–182.

We present the first polynomial-time approximation schemes (PTASes) for the following subset-connectivity problems in edge-weighted graphs of bounded genus: Steiner tree, low-connectivity survivable-network design, and subset TSP. The schemes run in O(n log n) time for graphs embedded on both orientable and non-orientable surfaces. This work generalizes the PTAS frameworks of Borradaile, Klein, and Mathieu [BMK07, Kle06] from planar graphs to bounded-genus graphs: any future problems shown to admit the required structure theorem for planar graphs will similarly extend to bounded-genus graphs.

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Related papers:
SteinerGenus_Algorithmica (Polynomial-Time Approximation Schemes for Subset-Connectivity Problems in Bounded-Genus Graphs)

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Last updated June 13, 2024 by Erik Demaine.